A particle moves on a straight path such that its displacement (in metre) at time (in…
MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A particle moves on a straight path such that its displacement x (in metre) at time t (in second) is given by
x=t3−6t2+9t+5.
Consider the time interval 0≤t≤5s.
(i) Obtain the expression for the instantaneous velocity v(t) of the particle.
(ii) Determine all instants within the given interval at which the particle momentarily comes to rest.
(iii) Calculate the displacement of the particle at each instant found in part (ii).
(iv) Identify the sub-intervals of time (within 0 to 5s) during which the particle moves opposite to the positive x-direction.